Find the Product (3a+b)^2

${(3 a + b)}^{2}$

Step 1

Rewrite ${(3 a + b)}^{2}$ as $(3 a + b) (3 a + b)$ .

$(3 a + b) (3 a + b)$

Step 2

Expand $(3 a + b) (3 a + b)$ using the FOIL Method.

Apply the distributive property.

$3 a (3 a + b) + b (3 a + b)$

Apply the distributive property.

$3 a (3 a) + 3 a b + b (3 a + b)$

Apply the distributive property.

$3 a (3 a) + 3 a b + b (3 a) + b \cdot b$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 a \cdot a + 3 a b + b (3 a) + b \cdot b$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$3 \cdot 3 (a \cdot a) + 3 a b + b (3 a) + b \cdot b$

Multiply $a$ by $a$ .

$3 \cdot 3 a^{2} + 3 a b + b (3 a) + b \cdot b$

Multiply $3$ by $3$ .

$9 a^{2} + 3 a b + b (3 a) + b \cdot b$

Rewrite using the commutative property of multiplication.

$9 a^{2} + 3 a b + 3 b a + b \cdot b$

Multiply $b$ by $b$ .

$9 a^{2} + 3 a b + 3 b a + b^{2}$

Add $3 a b$ and $3 b a$ .

Move $b$ .

$9 a^{2} + 3 a b + 3 a b + b^{2}$

Add $3 a b$ and $3 a b$ .

$9 a^{2} + 6 a b + b^{2}$